Discussion
The dimensions of an open box are 50 cm, 40 cm, and 23 cm. Its thickness is 3 cm. If 1 cubic cm of metal used in the box weighs 0.5 gms, find the weight of the box.
Answer: B
The metal is what lies between the outer box and the hollow inside it. The box is open, so only the depth loses one thickness, while the length and breadth lose two.
\[ V_{\text{outer}} = 50 \times 40 \times 23 = 46{,}000 \text{ cm}^{3} \]
\[ V_{\text{inner}} = (50-6)(40-6)(23-3) = 44 \times 34 \times 20 = 29{,}920 \text{ cm}^{3} \]
\[ V_{\text{metal}} = 46{,}000 - 29{,}920 = 16{,}080 \text{ cm}^{3} \]
\[ \text{weight} = 16{,}080 \times 0.5 = 8040 \text{ g} = 8.04 \text{ kg} \]
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